The White House has thrown its weight behind a proposal to raise the federal minimum wage to at least $10 an hour.

“The president has long supported raising the minimum wage so hard-working Americans can have a decent wage for a day’s work to support their families and make ends meet,” a White House official said.

President Obama, the official continued, supports the Harkin-Miller bill, also known as the Fair Minimum Wage Act, which would raise the federal minimum wage to $10.10 an hour, from its current $7.25.

The legislation is sponsored in the Senate by Tom Harkin of Iowa and in the House by George Miller of California, both Democrats. It would raise the minimum wage — in three steps of 95 cents each, taking place over two years — to $10.10, and then index it to inflation. The legislation will probably be coupled with some tax sweeteners for small businesses, traditionally the loudest opponents of increases to the minimum wage.

“The combination of an increase to $10.10 and some breaks for small business on expensing unite virtually the whole Democratic caucus, and we are prepared to move forward shortly,” said Senator Charles E. Schumer of New York, the Senate’s third-ranking Democrat.

Jason Furman, the chairman of the president’s Council of Economic Advisers, attended a Senate luncheon on Thursday with a focus on raising the minimum wage. One official at the luncheon said that some Democratic senators from more conservative states favored an increase to $9 an hour, but including the expensing provision was enough of a sweetener to bring them behind the $10.10 proposal.

Under that provision, small businesses would be able to deduct the total cost of investments in equipment or expansions, up to a maximum of $500,000 in the first year. Including such a provision helped persuade the Senate to vote overwhelmingly in favor of the last two minimum wage increases.

Democratic strategists say they are backing a higher minimum wage to help lift millions of low-wage workers at a time of increasing income inequality. Some also acknowledge that pushing a higher minimum wage is a way to put Republicans on the spot — caught between a business lobby and many conservatives who oppose an increased minimum wage and a public that strongly supports a higher minimum.

In his State of the Union speech in February, Mr. Obama called for a federal minimum wage of $9 an hour. But there has been little movement in Washington on that front, despite action at the state level. Some states set their minimum wage above the federal minimum, and in September, California passed a law that will steadily raise its minimum wage to $10 an hour by 2016.

Washington State currently has the highest state minimum wage at $9.19 an hour, a level indexed to inflation. Some cities have higher wages, including San Francisco, where the wage minimum is $10.55. On Tuesday, New Jersey voters approved a constitutional amendment, by a margin of 61 percent to 39 percent, that will raise the minimum wage to $8.25 an hour on Jan. 1, from $7.25. That measure includes annual increases based on inflation.

On March 15, the House voted 233 to 184 against a proposal to raise the minimum wage to $10.10 by 2015. The proposal came as an amendment to a job-training bill, and all 227 Republican members voted against the increase.

In July, on the fourth anniversary of the most recent minimum wage increase, Mr. Harkin and Mr. Miller stepped up their effort, citing a poll by Hart Research that found that 80 percent of Americans support increasing the minimum to $10.10. The Hart poll found that 92 percent of Democrats, 80 percent of independents and 62 percent of Republicans backed their proposal.

Mr. Miller said that he was confident that the House would vote to approve a higher minimum wage next summer because he thought several dozen Republicans would back the measure for fear of angering moderate-income voters as the Congressional elections approach.

Economists are somewhat more divided than the public about the effects of a minimum-wage increase, with conservatives concerned that raising the cost of labor could reduce the total number of low-wage workers employed.

But at least one well-regarded study found that raising the minimum wage increased employment of low-wage workers.

A version of this article appears in print on November 8, 2013, on page B3 of the New York edition with the headline: $10 Minimum Wage Proposal Has Growing Support From White House. Order Reprints|Today's Paper|Subscribe